Calling trading a zero-sum game shows a fundamental lack of understanding of finance. We may have very negative views on the industry, but it exists because it serves many fundamental (and necessary) functions, including:
* Accuracy in pricing shares (and it is important to know the actual value of a company for many reasons)
* Enable market participation. In many illiquid OTC markets, it is all but impossible for anyone outside large institutional players to participate. More trading = lower transaction costs, more transparency, and ability for the little guy (me) to join the action
* Liquidity. And yes, this is very important. It is a common answer because it is a good one
* The same security can be worth different amounts to different people. By definition this precludes it from being zero sum (this statement is of course subject to what school of financial theory you subscribe to)
* Performance measurement. Stock options have gotten a lot of bad press, but compensating a CEO according to lets say, revenue, is much less unbiased and can lead to worse outcomes (e.g., grows business in unattractive segments or over-invests to boost top line)
* Others
The above are in no way MECE and overlap in many ways. Markets can definitely be better, but calling it a zero-sum game or completely value-less to society is a bit too far.